Mass testing to identify and isolate infected individuals is a promising approach for reducing harm from the next acute respiratory virus pandemic, potentially avoiding the need for indiscriminate social distancing measures whilst averting hospitalizations and deaths. To understand scenarios where mass testing might or might not be a viable intervention, here we modelled how effectiveness depends both on characteristics of the pathogen (R0, time to peak viral load) and on the testing strategy (limit of detection, testing frequency, test turnaround time, adherence). We base time-dependent test sensitivity and time-dependent infectiousness on an underlying viral load trajectory model. We show that given moderately high public adherence, achievable frequent testing can prevent as many transmissions as more costly interventions such as school or business closures. With very high adherence and fast, frequent, and more sensitive testing, we show that most respiratory virus pandemics could be controlled with mass testing alone.